Superconformal Chern-Simons Theories and AdS_4/CFT_3 Correspondence

Understand

We discuss the N=2 superspace formulation of the N=8 superconformal Bagger-Lambert-Gustavsson theory, and of the N=6 superconformal Aharony-Bergman-Jafferis-Maldacena U(N)xU(N) Chern-Simons theory.

• In particular, we prove the full SU(4) R-symmetry of the ABJM theory.
• We then consider orbifold projections of this theory that give non-chiral and chiral (U(N)xU(N))^n superconformal quiver gauge theories.
• We argue that these theories are dual to certain AdS_4 x S^7/(Z_n x Z_k) backgrounds of M-theory.